The broad long-term objectives of this work are to develop and apply theoretical models to analyze complementary interactions formed during protein folding and binding. The ability of molecules to recognize one another with appropriate affinity and specificity is central to biology and medicine. The clinical activity of pharmaceutical agents is due largely to their ability to recognize and interfere with one or a small number of molecular targets; undesirable side effects are frequently caused by lack of specificity for the correct target. An important area of research involves understanding the design principles of natural protein molecules and developing tools to engineer modified or entirely new molecules by similar principles. The current proposal focuses on (1) further developments in methodology for the study and engineering of molecular structures and binding partners and (2) applications to particular biological molecules of interest. Current algorithms efficiently search side chain rotameric space when the backbone is fixed; we propose new methods to allow incorporation of backbone degrees of freedom or docking degrees of freedom as well. We have previously developed electrostatic optimization techniques that allow computation of idealized complementary binding partners, whose shape and charge distribution lead to high affinity binding. We propose to extend these methods to allow the design of actual ligand molecules that approach the idealized shape and charge distribution. Moreover, while high affinity or stability has been the focus of many design studies, we propose to develop methods that engineer in specificity as well. We will then apply this approach to investigations of the well studied Arc repressor and of proteins involved in phosphate recognition in signal transduction, and we will collaborate with experimentalists who are experts in these systems and will carry out parallel studies.